Haitao ZOU

I’m now a Post-Doc in Bielefeld University, sponsored by SFB-TRR 358

“Integral Structures in Geometry and Representation Theory”.

I was a PhD student in SCMS, Fudan University, supervised by Zhiyuan Li.

My research interests include

Algebraic Geometry (especially on K3 surface and its higher-dimensional analogue);
$p$-adic Geometry ($p$-adic cohomology theories, etc)

news

Sep 13, 2026	A new erratum to A note on Fourier–Mukai partners of abelian varieties over positive characteristic fields is now posted on the publications page. The converse implication in Proposition 4.5 of that paper is false — Ogus’s Torelli theorem gives a bijection on isomorphism classes, which does not realize a prescribed crystalline isometry — and the erratum gives a counterexample over $\overline{\mathbb{F}}_5$: supersingular abelian surfaces $A \not\cong B$ related by a degree-2 isogeny, with isomorphic abelian crystals but inequivalent derived categories. The surface theorem, Theorem 4.6, does not use the erroneous converse and stands unchanged. This note replaces the earlier addendum, whose strong-approximation argument is withdrawn.
Sep 12, 2026	Full-text HTML versions of my papers are now available alongside the PDFs — look for the HTML button on the publications page. They are generated from the LaTeX sources with LaTeXML, the same converter arXiv uses, so the mathematics is real text rather than images: it reflows on a phone, and it can be searched, copied and read by a screen reader.
Aug 31, 2026	I have added an Ongoing Papers section to this page, listing work that is written up or nearly written up but not yet posted. As open problems are increasingly attacked with AI assistance, it seems worth stating publicly what is already in preparation, so that the effort is not duplicated. Each entry gives its current status, the month it was last updated, and an abstract.

Selected Papers

All publications

MTHK

Monodromy rank and the semisimple Mumford–Tate conjecture for hyper-Kähler varieties

Zhichao Tang and Haitao Zou

submitted , Feb 2026

available at arXiv:2602.19835

arXiv Bib HTML PDF

@article{TZ26,
  title = {Monodromy rank and the semisimple Mumford–Tate conjecture for hyper-Kähler varieties},
  author = {Tang, Zhichao and Zou, Haitao},
  note = {available at arXiv:2602.19835},
  year = {2026},
  month = feb,
}

NagaiConj

Arithmetic monodromy of hyper-Kähler varieties over p-adic fields

Kazuhiro Ito, Tetsushi Ito, Teruhisa Koshikawa, Teppei Takamatsu, and Haitao Zou

submitted , Jul 2025

available at arXiv:2507.13713

arXiv Bib HTML PDF

@article{IIKTZ25,
  title = {Arithmetic monodromy of hyper-Kähler varieties over p-adic fields},
  author = {Ito, Kazuhiro and Ito, Tetsushi and Koshikawa, Teruhisa and Takamatsu, Teppei and Zou, Haitao},
  note = {available at arXiv:2507.13713},
  year = {2025},
  month = jul,
}

PointedShaf

Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture

Lie Fu, Zhiyuan Li, Teppei Takamatsu, and Haitao Zou

Peking Mathematical Journal, May 2025

Online Published

DOI arXiv Bib HTML PDF

@article{FLTZ23,
  title = {Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture},
  author = {Fu, Lie and Li, Zhiyuan and Takamatsu, Teppei and Zou, Haitao},
  journal = {Peking Mathematical Journal},
  note = {Online Published},
  year = {2025},
  month = may,
  doi = {10.1007/s42543-026-00122-9},
}

shafarevich

Unpolarized Shafarevich conjectures for hyper-Kähler varieties

Lie Fu, Zhiyuan Li, Teppei Takamatsu, and Haitao Zou

Algebraic Geometry, 13 (5), 598–638, 2026

DOI arXiv PDF
derivedisog

Derived isogenies and isogenies for abelian surfaces

Zhiyuan Li and Haitao Zou

Algebra & Number Theory, 20(2026) (6), 1185-1234, May 2026

DOI arXiv HTML PDF

OG6

Supersingular O’Grady varieties of dimension six

Lie Fu, Zhiyuan Li, and Haitao Zou

International Mathematics Research Notices, 2022 (11), 8769–8802, Jun 2022

DOI arXiv Bib PDF

@article{FLZ20,
  title = {Supersingular O’Grady varieties of dimension six},
  author = {Fu, Lie and Li, Zhiyuan and Zou, Haitao},
  journal = {International Mathematics Research Notices},
  volume = {2022},
  number = {11},
  pages = {8769--8802},
  year = {2022},
  month = jun,
  issn = {1073-7928},
  eissn = {1687-0247},
  publisher = {Oxford University Press},
  doi = {10.1093/imrn/rnaa349},
  url = {https://doi.org/10.1093/imrn/rnaa349},
}

Ongoing Papers

Work in preparation, listed so that it is clear what is already being done. Draft ready means a complete draft exists and I am happy to send it on request — just email me.

In prep

Semisimplicity, purity and Mumford–Tate conjecture for hyper-Kähler varieties

Kazuhiro Ito and Haitao Zou

In preparation, Draft ready, August 2026

Abs

We prove that every $\ell$-adic Galois representation arising from the cohomology of a projective hyper-Kähler variety over a field finitely generated over $\mathbb{Q}$ is semisimple. This yields the Mumford–Tate conjecture for all hyper-Kähler varieties, without restrictions on deformation type. As applications, we further prove the weight–monodromy conjecture in every degree for hyper-Kähler varieties over $p$-adic fields. We also establish an integral refinement of strong compatibility in the sense of Noot and Kisin–Zhou for the associated Mumford–Tate-valued Weil–Deligne representations.
In prep

$\mathbb{Q}$-factorial simultaneous terminalizations for families of primitive symplectic varieties

Chen Jiang, Zhiyuan Li, and Haitao Zou

In preparation, Draft ready, July 2026

Abs

We prove that every $\mathbb{Q}$-factorial projective locally trivial family of primitive symplectic varieties admits a $\mathbb{Q}$-factorial simultaneous terminalization after a finite base change. Over a smooth complex curve, such a terminalization can be obtained after a finite etale base change whose degree is bounded in terms of the number of crepant divisors in a single fiber. Over an arbitrary reduced base, a finite surjective base change suffices; when the base is normal, the cover may be chosen etale. The proof uses finite monodromy of crepant divisors, relative extraction, polarized deformation, and a curve-completion argument via the minimal model program. As an application, we extend the pointed Shafarevich finiteness theorem to primitive symplectic varieties that are not necessarily terminal.
In prep

F-splitting heights of good reductions of hyper-Kähler varieties of dimension at least four

Haitao Zou

In progress, September 2026

Abs

Let $X$ be a hyper-Kähler variety of dimension at least four over a $p$-adic field admitting good reduction, and let $X_0$ denote its special fibre. We study the geometry of $X_0$ through its Frobenius splitting behaviour, and in particular through the quasi-$F$-split height in the sense of Yobuko. Our main result is that for such a reduction the three conditions – quasi-$F$-splitting, $F$-splitting, and the Hodge–Witt property in the sense of Illusie–Raynaud – are equivalent; equivalently, the quasi-$F$-split height of $X_0$ is either $1$ or $\infty$. The dimension hypothesis is essential: for a K3 surface the quasi-$F$-split height agrees with the Artin–Mazur height and attains every value from $1$ to $10$, so that quasi-$F$-splitting and the Hodge–Witt property are both strictly weaker than $F$-splitting.